Simulation of finite-strain inelastic phenomena governed by creep and plasticity

Abstract

Inelastic mechanical behavior plays an important role in many applications in science and engineering. Phenomenologically, this behavior is often modeled as plasticity or creep. Plasticity is used to represent the rate-independent component of inelastic deformation and creep is used to represent the rate-dependent component. In several applications, especially those at elevated temperatures and stresses, these processes occur simultaneously. In order to model these process, we develop a rate-objective, finite-deformation constitutive model for plasticity and creep. The plastic component of this model is based on rate-independent \(J_2\) plasticity, and the creep component is based on a thermally activated Norton model. We describe the implementation of this model within a finite element formulation, and present a radial return mapping algorithm for it. This approach reduces the additional complexity of modeling plasticity and creep, over thermoelasticity, to just solving one nonlinear scalar equation at each quadrature point. We implement this algorithm within a multiphysics finite element code and evaluate the consistent tangent through automatic differentiation. We verify and validate the implementation, apply it to modeling the evolution of stresses in the flip chip manufacturing process, and test its parallel strong-scaling performance.